LearningGraphBased Quantum Algorithm for kdistinctness
Abstract
We present a quantum algorithm solving the $k$distinctness problem in $O(n^{12^{k2}/(2^k1)})$ queries with a bounded error. This improves the previous $O(n^{k/(k+1)})$query algorithm by Ambainis. The construction uses a modified learning graph approach. Compared to the recent paper by Belovs and Lee arXiv:1108.3022, the algorithm doesn't require any prior information on the input, and the complexity analysis is much simpler. Additionally, we introduce an $O(\sqrt{n}\alpha^{1/6})$ algorithm for the graph collision problem where $\alpha$ is the independence number of the graph.
 Publication:

arXiv eprints
 Pub Date:
 May 2012
 arXiv:
 arXiv:1205.1534
 Bibcode:
 2012arXiv1205.1534B
 Keywords:

 Quantum Physics
 EPrint:
 19 pages, 2 figures, major changes